$\frac{3}{2}+\frac{1}{4}=\frac{3\times2}{2\times2}+\frac{1}{4}=\frac{6}{4}+\frac{1}{4}=\frac{7}{4}=1\ \frac{3}{4}$

$1+\left(\frac{1}{2}+\frac{1}{4}\right)=1+\left(\frac{2}{4}+\frac{1}{4}\right)=1\ \frac{3}{4}$

$\frac{3}{2}+\frac{1}{4}=\frac{4}{6}=\frac{4:2}{6:2}=\frac{2}{3}$

$1+\left(\frac{1}{2}+\frac{1}{4}\right)=1+\frac{2}{6}=1\ \frac{2}{6}=1\ \frac{1}{3}$